The recent achievements in the formation and manipulation of ultracold polar molecules have opened the gate to exciting new studies in several fields of physical sciences. Polar molecules could find uses in quantum information science and in precision measurements, while dense samples could provide a fertile ground for novel quantum gases because of their long-range and anisotropic interactions. I will discuss how the formation of ultracold molecules can be increased near a Feshbach resonance by several orders of magnitude. I will also present some applications of ultracold polar molecules, such as their potential use for quantum information or high-precision measurements. Finally, I will explore how two ultracold polar molecules interact. Until now, stable dipolar gases were thought to require a repulsive dipole-dipole interaction. However, to observe interesting new correlations and condensed matter phases, attractive interactions are needed. Here, we investigate how meta-stable one-dimensional (1-D) samples of ultracold polar molecules could be created with attractive long-range dipole-dipole interaction. We show that a repulsive barrier due to a strong quadrupole interaction can stabilize a gas of ultracold KRb molecules and even lead to long-range wells supporting bound states. The properties of these wells can be controlled by external electric fields, allowing the formation of long chains of KRb polymers, and the further study of Luttinger liquid transition.